Abstract
Let R= k[ x 1,…, x n ] be the polynomial ring in n independent variables, where k is a field of characteristic zero. In this work, we will describe the multiplicities of the characteristic cycle of the local cohomology modules H I r ( R) supported on a squarefree monomial ideal I⊆ R in terms of the Betti numbers of the Alexander dual ideal I ∨. From this description we deduce a Gorensteinness criterion for the quotient ring R/ I. On the other side, we give a formula for the characteristic cycle of the local cohomology modules H p p(H I r(R)) , where p is any homogeneous prime ideal of R. This allows us to compute the Bass numbers of H I r ( R) with respect to any prime ideal and describe its associated primes.
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